1997/04/24 by Eric M. Rains, Rains, Eric M. · 6 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9704043
13 pages, AMSTeX
arxiv created 1997/04/24 · openalex publication_date 1997/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then show that this bound can only be attained when the code either is of even length, or is of length 3 or 5. We next consider questions of uniqueness, showing that the optimal code of length 2 or 4 is unique (implying that the well-known one-qubit-in-five single-error correcting code is unique), and presenting nonadditive optimal codes of all greater even lengths. Finally, we compute the full automorphism group of the more important distance 2 codes, allowing us to determine the full automorphism group of any GF(4)-linear code.